Gauge amplitude identities by on-shell recursion relation in S-matrix program

Using only the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relation we prove color-order reversed relation, U(1)-decoupling relation, Kleiss-Kuijf (KK) relation and Bern-Carrasco-Johansson (BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color-ordered basis from (n - 2)! to (n - 3)!. Our proof gives also its physical interpretation as the mysterious bonus relation with 1/z(2) behavior under suitable on-shell deformation for no adjacent pair. (C) 2010 Elsevier B.V. All rights reserved.